Remarks on the one-point density of Hele-Shaw $β$-ensembles
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909571886350336 |
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| author | Ameur, Yacin Troedsson, Erik |
| author_facet | Ameur, Yacin Troedsson, Erik |
| contents | In this note we prove equicontinuity for the family of one-point densities with respect to a two-dimensional Coulomb gas at an inverse temperature $β\ge 1/2$ confined by an external potential of Hele-Shaw (or quasi-harmonic) type. As a consequence, subsequential limiting Lipschitz continuous densities are defined on the microscopic scale. There are several additional results, for example comparing the one-point density with the thermal equilibrium density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on the one-point density of Hele-Shaw $β$-ensembles Ameur, Yacin Troedsson, Erik Probability Mathematical Physics In this note we prove equicontinuity for the family of one-point densities with respect to a two-dimensional Coulomb gas at an inverse temperature $β\ge 1/2$ confined by an external potential of Hele-Shaw (or quasi-harmonic) type. As a consequence, subsequential limiting Lipschitz continuous densities are defined on the microscopic scale. There are several additional results, for example comparing the one-point density with the thermal equilibrium density. |
| title | Remarks on the one-point density of Hele-Shaw $β$-ensembles |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2402.13882 |